Journal article Open Access

On Completeness in Metric Spaces and Fixed Point Theorems

Valentin Gregori; Juan José Miñana; Bernardino Roig; Almanzor Sapena

MARC21 XML Export

<?xml version='1.0' encoding='UTF-8'?>
<record xmlns="">
  <datafield tag="653" ind1=" " ind2=" ">
    <subfield code="a">G-complete metric space</subfield>
  <datafield tag="653" ind1=" " ind2=" ">
    <subfield code="a">weak G-complete metric space</subfield>
  <controlfield tag="005">20210617014820.0</controlfield>
  <datafield tag="500" ind1=" " ind2=" ">
    <subfield code="a">This is a preprint of the publication available from This work is also supported by project PGC2018-095709-B-C21 (MCIU/AEI/FEDER, UE), and PROCOE/4/2017 (Govern Balear, 50% P.O. FEDER 2014-2020 Illes Balears).</subfield>
  <controlfield tag="001">4967530</controlfield>
  <datafield tag="700" ind1=" " ind2=" ">
    <subfield code="u">University of the Balearic Islands</subfield>
    <subfield code="a">Juan José Miñana</subfield>
  <datafield tag="700" ind1=" " ind2=" ">
    <subfield code="u">Polytechnic University of Valencia</subfield>
    <subfield code="a">Bernardino Roig</subfield>
  <datafield tag="700" ind1=" " ind2=" ">
    <subfield code="u">Polytechnic University of Valencia</subfield>
    <subfield code="a">Almanzor Sapena</subfield>
  <datafield tag="856" ind1="4" ind2=" ">
    <subfield code="s">297026</subfield>
    <subfield code="z">md5:0bca8bf911b729a909856d1f083ae20d</subfield>
    <subfield code="u"> in mathematics_2018.pdf</subfield>
  <datafield tag="542" ind1=" " ind2=" ">
    <subfield code="l">open</subfield>
  <datafield tag="260" ind1=" " ind2=" ">
    <subfield code="c">2018-10-08</subfield>
  <datafield tag="909" ind1="C" ind2="O">
    <subfield code="p">openaire</subfield>
    <subfield code="o"></subfield>
  <datafield tag="909" ind1="C" ind2="4">
    <subfield code="c">142</subfield>
    <subfield code="v">73</subfield>
    <subfield code="p">Results in Mathematics</subfield>
  <datafield tag="100" ind1=" " ind2=" ">
    <subfield code="u">Polytechnic University of Valencia</subfield>
    <subfield code="a">Valentin Gregori</subfield>
  <datafield tag="245" ind1=" " ind2=" ">
    <subfield code="a">On Completeness in Metric Spaces and Fixed Point Theorems</subfield>
  <datafield tag="536" ind1=" " ind2=" ">
    <subfield code="c">779776</subfield>
    <subfield code="a">Robotics Technology for Inspection of Ships</subfield>
  <datafield tag="540" ind1=" " ind2=" ">
    <subfield code="u"></subfield>
    <subfield code="a">Creative Commons Attribution 4.0 International</subfield>
  <datafield tag="650" ind1="1" ind2="7">
    <subfield code="a">cc-by</subfield>
    <subfield code="2"></subfield>
  <datafield tag="520" ind1=" " ind2=" ">
    <subfield code="a">&lt;p&gt;Complete ultrametric spaces constitute a particular class of the so called, recently, G-complete metric spaces. In this paper we characterize a more general class called weak G-complete metric spaces, by means of nested sequences of closed sets. Then, we also state a general fixed point theorem for a self-mapping of a weak G-complete metric space. As a corollary, every asymptotically regular self-mapping of a weak G-Complete metric space has a fixed point.&lt;/p&gt;</subfield>
  <datafield tag="773" ind1=" " ind2=" ">
    <subfield code="n">doi</subfield>
    <subfield code="i">isVersionOf</subfield>
    <subfield code="a">10.5281/zenodo.4967529</subfield>
  <datafield tag="024" ind1=" " ind2=" ">
    <subfield code="a">10.5281/zenodo.4967530</subfield>
    <subfield code="2">doi</subfield>
  <datafield tag="980" ind1=" " ind2=" ">
    <subfield code="a">publication</subfield>
    <subfield code="b">article</subfield>
All versions This version
Views 2222
Downloads 1717
Data volume 5.0 MB5.0 MB
Unique views 2121
Unique downloads 1616


Cite as